Father-son mathematics team tackles cryptocurrencies and stock market vulnerabilities

The most exciting professional collaboration in Gunduz Caginalp’s 34-year career at Pitt came this year, when he published a paper co-authored with his 24-year old son and Department of Mathematics visiting scholar, Carey Caginalp (A&S ’11). He said the opportunity was one he had anticipated since 2004, when Carey first stepped foot on the Pitt campus as a child prodigy.

“Carey took an interest in math at a very early age,” said Gunduz, a mathematics professor who has worked with world-renowned economists, including Nobel Laureate Vernon Smith, in the study of theoretical mathematical concepts. “My wife started homeschooling him around age 5 and by age 6 he had finished most of the math and science curriculum through seventh grade,” Gunduz said.

The paper, titled “Valuation, Liquidity Price and Stability of Cryptocurrencies,” ran in Proceedings of the National Academy of Sciences. It isn’t Carey’s first publication, but going through the process with the man who’s nurtured his natural flair for math since childhood makes it one of the most important, particularly since the discipline was never forced upon him.

“One of my earliest memories was prime numbers,” said Carey. “How they weren’t divisible by other numbers, whether there was a biggest prime number, things like that.”

After flying through high school math, Carey took his first course at Pitt — Discrete Math Structures — at age 10 while continuing homeschooling for literature, history and the social sciences. By his 17th birthday, he had finished a rigorous Bachelor of Philosophy degree in mathematics that included a thesis on an applied math concept. He was also on his way to a PhD program at Brown University and on pace to publish his first and second research papers.

“Imagine a circle with a small exit slit and you have a particle moving around in there randomly,” Carey said, describing his thesis concept. “The idea is how long, on average, will it take the particle to escape through that small gate? I showed the exact formula for how long it would take for any sized gate.”

Carey earned his PhD from Brown and last fall was an instructor at Carnegie Mellon University. In addition to his current work at Pitt, he also is a visiting affiliated scholar at Chapman University’s Economic Science Institute in California. 

Working together

For Gunduz, Carey’s evolution brought not only a sense of pride but an incredibly valuable set of skills in addition to his own to tackle difficult problems.

“Carey has expertise in pure probability that I hadn’t been applying to asset markets,” he said. So, the father-son team partnered up.

The idea of studying cryptocurrency values occurred to Carey last year during one of the many spike-and-drop cycles tied to the most popular digital currency, bitcoin.

“I was following developments in the news, watching pricing and volatility in bitcoin, and it struck my interest as to what this is actually worth, how is it potentially being used, what factors are influencing people to buy, trade or sell,” Carey said. “I had another look into it after looking at one of my father’s papers, then I had the idea that it’s tied to our notion of liquidity,” he said.

That research, by Gunduz and Indiana University of Pennsylvania Mathematics Professor Donald Balenovich, showed that assets without specific values, such as some stocks, are ultimately determined by the total number of units available for sale, the amount of cash available in that market or how much liquidity the asset holds.

This notion, in addition to an experiment on buying behaviors that encourage marketplace bubbles co-authored by Gunduz, Chapman University economist David Porter and Chapman University’s Vernon Smith, gave the Caginalps a solid basis to conclude that bitcoin — and cryptocurrencies in general — will not gain enough stability to be widely used as a standard currency and may only be useful for fringe buyers and savvy traders.

So far, the valuation paper and its theories have attracted the attention of The Wall Street Journal, Bloomberg, NPR and other news sites across the globe. It also sparked an invitation for both Gunduz and Carey from U.S. Securities and Exchange Commissioner Michael Piwowar to discuss cryptocurrency regulatory strategies during a March listening tour in Pittsburgh. 

Next for the Caginalps is teaming up on two more papers, one on stock market volatility and another examining why so-called “rare” steep drops such as the 2008 recession aren’t as rare as classical theories imply. The plan is for these next two papers to complement their first paper, creating a father-son, three-part series on finance.

“I’ve had a lot of collaborators over the years, but this experience is just about the most wonderful for me,” Gunduz said.

— Deb Todd, photography by Tom Altany